Find the determinant of the matrix.Expand by cofactors on the row or column that appears to make the computations easiest. $$\left[ \begin{array} { c c c }
9 & 8 & - 2 \
2 & 2 & 0 \
- 9 & 8 & 2
\end{array} \right]$$
A)-64
B)-62
C)-66
D)-65
E)-63

Question

Find the determinant of the matrix.Expand by cofactors on the row or column that appears to make the computations easiest.​ $$\left[ \begin{array} { c c c } 
9 & 8 & - 2 \
2 & 2 & 0 \
- 9 & 8 & 2
\end{array} \right]$$ ​
A)-64
B)-62
C)-66
D)-65
E)-63

Quizplus · Accepted Answer

Expanding by cofactors along the third column, where the element in the second row and third column is 0, simplifies the calculation. The determinant is $9(2*2 - 8*0) - 8(2*0 - (-9)*2) - 2(2*8 - 2*(-9)) = 9*4 - 8*(-18) - 2*34 = 36 + 144 - 68 = 112$. However, there seems to be a mistake in my calculation as none of the provided options match the result. Let's correct the calculation:Expanding by cofactors along the third column for easier computation, the determinant is:$$= (-2) \cdot \left| \begin{array}{cc} 2 & 2 \ -9 & 8 \end{array} \right| - 0 \cdot \left| \begin{array}{cc} 9 & 8 \ -9 & 8 \end{array} \right| + 2 \cdot \left| \begin{array}{cc} 9 & 8 \ 2 & 2 \end{array} \right|$$$$= (-2) \cdot (2*8 - 2*(-9)) + 0 + 2 \cdot (9*2 - 8*2)$$$$= (-2) \cdot (16 + 18) + 2 \cdot (18 - 16)$$$$= (-2) \cdot 34 + 2 \cdot 2$$$$= -68 + 4$$$$= -64.$$So, the correct calculation indeed results in -64, matching option A.

Find the Determinant of the Matrix [98−2220−982]\left[ \begin{array} { c c c } 9 & 8 & - 2 \\2 & 2 & 0 \\- 9 & 8 & 2\end{array} \right]​92−9​828​−202​​

Find the Determinant of the Matrix $\left[ \begin{array} { c c c } 9 & 8 & - 2 \\2 & 2 & 0 \\- 9 & 8 & 2\end{array} \right]$